## View abstract

### Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 14:00 ~ 14:35 UTC-3

## Random walk in a field of weakly killing exclusion particles

### Dirk Erhard

Consider a simple random walk, and independently of it the simple symmetric exclusion process on $\mathbb{Z}^d$. The random walk gets killed at rate epsilon when it shares a site with an exclusion particle. Using the relation to the parabolic Anderson model and the theory of regularity structures, I will present exact asymptotics for the survival probability of the random walk as epsilon tends to zero in dimension $d=3$. To establish these, precise bounds on the joint cumulants of the exclusion process are needed, which hold as soon as $d\geq 3$. I will also discuss what is missing to establish the corresponding result in $d=2$.